“My priority is to do well here. This has always been my club,” Wenger, who will celebrate 20 years at Arsenal on Saturday, told reporters.
“If I am free one day, why not? But I am concentrated on my job,” he said, referring to the England job.
The Football Association is looking for a new England manager after the shock end to Sam Allardyce’s 67-day stint following a newspaper investigation.
Wenger, whose contract with Arsenal runs out at the end of the season, said his managerial style has evolved through the years in his “love affair” with Arsenal.
“I have a passion for the game but I have the desire to be better tomorrow and yesterday,” Arsenal’s longest serving manager said.
“The way I manage today is not the same today as five years ago. How long can I do, I don’t know.
“I rule nothing out because I want to work and do well. I accept as well that it can finish tomorrow. You expect a love story to last forever.”
Wenger also thanked the club for backing him in crisis.
“My resilience and passion has helped the most, but also the board to stick by me and I believe this club is brave… That’s the quality that came out at good and bad moments and fought together,” he added.
Arsenal have picked up the pace after a slow start to the campaign and are on an eight-game unbeaten run in all competitions, including six victories.
They will hope to extend their streak when they face Burnley on Sunday.